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Theory and Modern Applications

Table 2 The absolute errors and relative errors of numerical solutions to Example 1 for \(h=1/19\) (i.e., \(m-1=18=6K\), \(K=3\))

From: A new parallel algorithm for solving parabolic equations

\(x_{j}\)

Algorithm 1 (t = 0.2)

Algorithm 1 (t = 0.4)

Algorithm 1 (t = 0.8)

A. E.

R. E.

A. E.

R. E.

A. E.

R. E.

0.11

0.3731e−3

1.7559e−2

0.5021e−3

1.9312e−2

0.7577e−3

1.9534e−2

0.21

0.6184e−3

1.5420e−2

0.8428e−3

1.7176e−2

1.2739e−3

1.7399e−2

0.31

0.8750e−3

1.5999e−2

1.1881e−3

1.7754e−2

1.7950e−3

1.7976e−2

0.42

0.9753e−3

1.5409e−2

1.3294e−3

1.7165e−2

2.0093e−3

1.7388e−2

0.52

1.0066e−3

1.5469e−2

1.3715e−3

1.7225e−2

2.0729e−3

1.7447e−2

0.63

0.9135e−3

1.5280e−2

1.2463e−3

1.7037e−2

1.8839e−3

1.7259e−2

0.73

0.7582e−3

1.5778e−2

1.0310e−3

1.7534e−2

1.5579e−3

1.7757e−2

0.84

0.5469e−3

1.7563e−2

0.7361e−3

1.9316e−2

1.1109e−3

1.9538e−2

0.95

0.1891e−3

1.7556e−2

0.2545e−3

1.9309e−2

0.3841e−3

1.9532e−2